Traveling waves for nonlinear Schrödinger equations

2024/06/06 by Baldelli, Laura, Bieganowski, Bartosz, Mederski, Jarosław
#35C07 #35J10 #35J20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.03910

Abstract

We look for traveling wave solutions to the nonlinear Schrödinger equation with a subsonic speed, covering several physical models with Sobolev subcritical nonlinear effects. Our approach is based on a variant of Sobolev-type inequality involving the momentum and we show the existence of its minimizers solving the nonlinear Schrödinger equation.

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